Discussion
Trace of a 3 × 3 matrix is 6. Two of its eigen values are 1 and 2. The third eigen value is :
Answer: C
The third eigenvalue is 3.
The trace of a square matrix equals the sum of its eigenvalues (counted with multiplicity). So
\[ \begin{aligned} \lambda_{1} + \lambda_{2} + \lambda_{3} &= 6 \\ 1 + 2 + \lambda_{3} &= 6 \\ \lambda_{3} &= 3 \end{aligned} \]
The option 6 is the trace itself, mistaken for an eigenvalue; 1 and 2 repeat the eigenvalues already given and would make the trace 4 or 5. Only 3 makes the three eigenvalues add up to the trace.
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